Photovoltaic cells produce a voltage that varies with current, cell operating condition, cell physics, cell defects, and cell illumination. One mathematical model for a photovoltaic cell, as illustrated in FIG. 1, models output current as:
                    I        =                              I            L                    -                                    I              0                        ⁢                          {                                                exp                  ⁡                                      [                                                                  q                        ⁡                                                  (                                                      V                            +                                                          I                              ⁢                                                                                                                          ⁢                                                              R                                S                                                                                                              )                                                                                            n                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                                                  ⁢                        T                                                              ]                                                  -                1                            }                                -                                                    V                +                                  I                  ⁢                                                                          ⁢                                      R                    S                                                                              R                                  S                  ⁢                                                                          ⁢                  H                                                      .                                              Equation        ⁢                                  ⁢        1            Where
IL=photogenerated current
RS=series resistance
RSH=shunt resistance
I0=reverse saturation current
n=diode ideality factor (1 for an ideal diode)
q=elementary charge
k=Boltzmann's constant
T=absolute temperature
I=output current at cell terminals
V=voltage at cell terminals
For silicon at 25° C., kT/q=0.0259 Volts.
Typical cell output voltages are low and depend on the band gap of the material used to manufacture the cell. Cell output voltages may be merely half a volt for silicon cells, far below the voltage needed to charge batteries or drive most other loads. Because of these low voltages, cells are typically connected together in series to form a module, or an array, having an output voltage much higher than that produced by a single cell.
Real-world photovoltaic cells often have one or more microscopic defects. These cell defects may cause mismatches of series resistance RS, shunt resistance RSH, and photogenerated current IL from cell to cell in a module. Further, cell illumination may vary from cell to cell in a system of photovoltaic cells, and may vary even from cell to cell in a module, for reasons including shadows cast by trees, bird droppings shadowing portions of a cell or module, dust, dirt, and other effects. These mismatches in illumination may vary from day to day and with time of day—a shadow may shift across a module during a day, and rain may wash away dust or dirt shadowing a cell.
From equation 1, output voltage is greatest at zero output current, and output voltage V falls off nonlinearly with increasing output current I. FIG. 2 illustrates the effect of increasing current drawn from a photovoltaic device at constant illumination. As current I is increased under constant illumination, voltage V falls off slowly, but as current I is increased to an output current near the photocurrent IL, output voltage V falls off sharply. Similarly, cell power, the product of current and voltage, increases as current I increases, until falling voltage V overcomes the effect of increasing current, whereupon further increases in current I drawn from the cell cause power P to decrease rapidly. For a given illumination, each cell, module, and array of cells and modules therefore has a maximum power point (MPP) representing the voltage and current combination at which output power from the device is maximized. The MPP of a cell, module, or array will change as temperature and illumination, and hence photo-generated current IL, changes. The MPP of a cell, module, or array may also be affected by factors such as shadowing and/or aging of the cell, module, or array.
A photovoltaic cell can be operated at or near its maximum power point by use of a Maximum Power Point Tracking (MPPT) controller. MPPT controllers are devices that determine an MPP voltage and current for a photovoltaic device connected to their input, and adjust their effective impedance to maintain the photovoltaic device at the MPP. MPPT controllers typically measure photovoltaic device voltage and current at a number of operating points, calculate power at each operating point from the voltage and current measurements, and determine which operating point is closest to the MPP.
It can be difficult to operate a number of photovoltaic cells at their MPP when the cells are electrically coupled together. For example, FIG. 3 illustrates four photovoltaic cells electrically coupled in a series string. Without diodes D1-D3 or other added circuitry, each of the cells must carry the same current. Variations in parameters such as photo-generated current IL, effective shunt resistance RSH, series resistance, and/or temperature between cells of a module or of an array described above may cause the maximum power point output current for one cell Cstrong in a string to be at a current well above the maximum power point output current Iweak for another cell Cweak in the string. In some arrays under some conditions, if Cstrong is operating at its MPP current, Cweak is subjected to a current above its MPP current, possibly resulting in damage to Cweak. Cweak may even reverse-bias—thereby consuming power instead of generating power, or blocking current flow from the better producing cells in the same string. The net effect is that power output from a panel or a series string of panels is limited by the performances of the poorer-producing cells in the series string.
Some prior solar panels have bypass diodes D1, D2, D3 at the module, at the cell, or at a group of cells, level, as illustrated in FIG. 3. The bypass diodes prevent possible damage to the weak cell Cweak resulting from excessive forward current. The bypass diodes also prevent Cweak from reverse-biasing and blocking current flow from better producing cells in the string, but, as the low producing cell and any other cells in the same group with the same bypass diode is bypassed, any power produced by Cweak and cells in its group is lost. Additionally, some power from the better producing cells is dissipated in the diode due to its forward voltage drop. As illustrated in FIG. 3, while some modules may provide bypass diodes such as D2 across individual cells, other modules or systems may provide diodes such as D1 across groups of cells, or even across entire modules, instead of across individual cells. Many crystalline silicon modules on the market today provide bypass diodes across “6-volt” sections of around a dozen cells.
Other systems are known, as illustrated in FIG. 40, that use distributed, per-panel, DC-DC converters 4002 or DC-AC microinverters to drive a common power-summing high-voltage bus 4004 as illustrated in FIG. 40. Each converter 4002 receives power from a solar module 4006, each module having many photovoltaic cells 4008, at whatever voltage and current that module 4006 is capable of generating and potentially at the MPP of that module, and converts and outputs the power onto the high-voltage power-summing bus 4004. Since modules are no longer connected in series, low production by one module does not interfere with production by high-performing modules. Further, potential power production by low-performing modules is summed on the bus and not wasted.
An issue with distributed, per-panel voltage converter architectures is that such architectures help to achieve MPP only at the panel level, but do not work at the individual cell level. For example, when even a single cell of a panel is cracked or partially shaded—the entire panel may not deliver the full potential power from the rest of the cells. Cells may also be mismatched through manufacturing variations, differential soiling, and aging as well as damage and shade. U.S. patent application publication number 2009/0020151 proposes variations on using local converters to drive DC or AC power-summing buses in parallel.
Yet another alternative is disclosed in U.S. patent application publication number 2008/0236648, in which power from groups of photovoltaic cells is fed into respective MPPT DC-DC converters to produce a current constant throughout all DC-DC converters of the array at a voltage at each converter that depends on power available from the attached photovoltaic device. The outputs of the DC-DC converters are connected in series.
It may also be difficult to operate multiple junctions in a multi junction photovoltaic cell at their respective maximum power points. Multi junction photovoltaic cells have two or more junctions of different types stacked vertically, and each junction is intended to respond to light of a different wavelength. For example, two junction photovoltaic cells typically have a top junction made of materials with large bandgap and thus having a relatively short favored wavelength and a maximum power point at relatively high voltage, and a bottom junction having a lower bandgap and thus having a relatively long favored wavelength and a maximum power point at relatively low voltage.
Cells of multi junction photovoltaic devices are often coupled electrically in series as they are formed, without bringing out a conductor from between the cells. While this construction simplifies connections to the cells, inefficiencies result for the same reasons that output of mismatched series-connected photovoltaic devices may be restricted; effective output current is determined by the lowest-current output of the stacked cells. This situation is aggravated by variations in color, or wavelength distribution, of received light, and by differences in types and efficiencies of the stacked cells. A given junction of a multi junction cell may also be damaged by excessive forward current unless a bypass device, such as a diode, is provided.
Multi-junction photovoltaic devices have been studied, including those having stacked cells with a low-resistance electrical contact to a boundary between junctions, and those having junctions brought out separately. For example, see McDonald, Spectral Efficiency Scaling of Performance Ratio for Multijunction Cells, 34 IEEE Photovoltaic Specialist Conference, 2009, pg. 1215-1220.